Trust the Process
Trust the process long enough to make improvements with hindsight.
The process is there to get you though without having to figure out how you'll get there, or where your collaborators are going at every step of the way. As Albert North Whitehead said “Civilization advances by extending the number of important operations which we can perform without thinking of them.” Process does this. The process is there to guide us when we are overwhelmed by or cannot see clearly the magnitude of what we are endeavoring to achieve together.
The status quo process, industry standard process, is everything that everyone who came before in the industry has figured out. They're good at this if their process became industry standard. You have no business having a process worse than industry standard. Go learn it.
They made it for themselves back then though and you're now in a different situation, so it won't be a perfect fit. But we can't go messing with it yet. We, as a team, don't know it well enough yet.
This is an important point that is easily missed so I'm going to say it twice. You are not in a position to improve a process that teh team is not experienced with. You are not in a position to improve a process that the team is not experienced with. You gotta give it a real shot, become competent practitioners before you can improve it for your particular situation. If you're doing Scrum, do it for real. Commit. Trust it. Get everyone on board and excited about getting good enough at Scrum to improve it for yourselves.
Start with a simple version. Document it. Train the teams.
Once the team is competent at it, I bet there will be a lot you won't want to change. But there will be a few opportunities that stand out. Build consensus around those with all the stakeholders, update the documentation and training, and make the improvements.
It's a different proces now though, so you'll have to document it, train the teams, to get competant. Mature.
Repeat forever.
Eventually you'll have something bespoke and beautiful that fits your teams like a glove. Then your teams will change, or the industry will change and you'll have to adapt, but you'll be practiced at that too.
You'll do great, if you trust the process.